We investigate how users touch arbitrary shapes. First, we performed semi-structured interviews with a fifteen-shape set as prop to identify touch strategies. Results reveal four main potential touch strategies, from which we devised nine mathematical candidate models. We investigate the ability of these models to predict human behaviour in a controlled experiment. We found that the center of a shape's bounding box best approximates a user's target location when touching arbitrary shapes. Our findings not only invite designers to use a larger variety of shapes, but can also be used to design touch interaction adapted to user behaviour using our model. As an example, they are likely to be valuable for the creation of applications exposing shapes of various complexities, like drawing applications.